Section 6.6: Interference
Interference occurs when two or more coherent waves overlap, producing a resultant wave pattern of alternating bright and dark regions.
- Constructive Interference: Waves are in phase; amplitudes add up → bright fringe.
- Destructive Interference: Waves are out of phase; amplitudes subtract → dark fringe.
- Path difference for constructive interference: \[ \Delta L = m \lambda, \quad m = 0,1,2,\dots \]
- Path difference for destructive interference: \[ \Delta L = \left(m + \frac{1}{2}\right) \lambda, \quad m = 0,1,2,\dots \]
- Fringe spacing (for double slit): \[ \Delta y = \frac{\lambda L}{d} \] where \(L\) = screen distance, \(d\) = slit separation.
Example: Double-slit Interference
Light of wavelength 500 nm passes through two slits separated by 0.25 mm. The screen is 2 m away. Find the fringe spacing.
Using \( \Delta y = \frac{\lambda L}{d} \): \( \Delta y = \frac{500 \times 10^{-9} \times 2}{0.25 \times 10^{-3}} = 4.0 \, \text{mm} \)
Practice Problems
- Two slits separated by 0.3 mm produce interference with wavelength 600 nm. Screen is 1.5 m away. Calculate fringe spacing.
- Find the order of the bright fringe at 3 mm from the central maximum if fringe spacing is 0.5 mm.
- Explain why coherent light sources are necessary for interference.
- Describe the effect on fringe spacing if the slit separation is doubled.
- Sketch a double-slit interference pattern and label constructive and destructive regions.